$2\mathrm{.}3.$ Evaluate the following without using a calculator:

$2\mathrm{.}3\mathrm{.}1.{\displaystyle \underset{1}{\overset{}{}}}\frac{dx}{x^2+x}.$

$2\mathrm{.}3\mathrm{.}2.{\displaystyle \underset{n=1}{\overset{}{}}}[cos(\frac{1}{n})-cos(\frac{1}{n+1})].$